Tarp assemblies are used to cover open top containers such as an open top truck box or truck trailer used in transport of granular material, hard goods and the like. The open top box or trailer has characteristics of economy of construction and ease of loading and unloading certain commodities but lacks the measure of protection afforded by a structurally enclosed truck trailer. Accordingly, tarp assemblies include a tarp for removably covering the top of the open top trailer to protect the contents thereof during transport or simply during storage. For aerodynamic considerations, the tarp is preferably tight fitting. Due to the size of the box and the tarp, preferably means are provided to simplify the covering and uncovering procedures permitting them to be accomplished by a single individual standing at ground level in a relatively short period of time.